Equivariant Gromov-Witten theory of one dimensional stacks

Abstract

In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is again governed by the 2-Toda hierarchy. In the ineffective case the decomposition conjecture of hep-th/0606034 is verified.

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Cited by in corpus (17)

• Localization in Gromov-Witten Theory and Orbifold Gromov-Witten Theory
• Integrable hierarchies and the mirror model of local CP1
• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies
• Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formula
• Towards an orbifold generalization of Zvonkine's $r$-ELSV formula
• Duality theorems for étale gerbes on orbifolds
• Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants
• A quantum Leray-Hirsch theorem for banded gerbes
• Generalized Mariño-Vafa Formula and Local Gromov-Witten Theory of Orbi-curves
• Higher genus relative and orbifold Gromov-Witten invariants of curves
• Localization and Gluing of Orbifold Amplitudes: The Gromov-Witten Orbifold Vertex
• BCFG Drinfeld-Sokolov Hierarchies and FJRW-Theory
• On the geometry of orbifold Gromov-Witten invariants
• Relations on Mbar_{g,n} via orbifold stable maps
• Gromov-Witten invariants of ${\mathrm{Sym}}^d{\mathbb{P}}^r$
• Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$